Initially, you need to go through the steps to find the cubes of numbers from 1 to 20. Also, you need to memorize the following table else you may find it difficult to find the cube root of a number. (Remember: The symbol ^ means “raise to” or “power of” the given number) 

Number Unit place of cube root 

     1^3   1

     2^3   8

     3^3   7

     4^3   4

     5^3   5

     6^3   6

     7 ^3   3

     8^3   2

     9^3      9

     0^3 0  

Finding the cube root by estimation you have to follow the following steps:

You are given the number 17576. Find its cube root by estimation method.

Step 1: First, you need to separate the numbers into a pair of three numbers from backward, depending upon the given number. Here, 576 is the first group (as we need to make a pair of three numbers from backward), and only the remaining number is 17, which is a two-digit number. 

Step 2: Let us constopicIder the number 576.

Its unit digit is 6. You have to refer to the above table and check what’s in the unit place, which ends with the number 6. From the table, we understand that the cube of the number 6 always ends with the number 6 at the unit’s place. We will fix 6 as our last digit. Remember this! We will use it later.

Step 3: Now, it is time to take the remaining numbers i.e. 17.

We know that the cube of one is one; a cube of the number 2 ends with the digit 8 and the cube of the number 3 ends with the number 7, in its unit’s place. 1^3= 1, 2^3 = 8, and  3^3=27  (the symbol “^” means to raise to the number).

PLEASE PAY CAREFUL ATTENTION NOW:

From the table, we understand that the cube of the number 2 ends with the digit 8, and the cube of the number 3 ends with the digit 7, that is, 2^3=8 and 3^3=27. 

Now, determine the number 17 falls between which cube numbers? The answer is 17 lies between 8 and 27, that is, 2^3=8 and 3^3=27 

Check which is the smallest number between 8 and 27, as 17 lies between the cube of 2  (cube is 8) and 3 (cube is 27). The smallest cube number is 8. Now, you will have to again check the table and see 8 is a cube of which number. The answer is 2. Hence, we retain 2 as our next number after selecting 6 in the unit’s place.

So, the tens-place number of the cube root of number 17576 is 2 and keep 6 as its unit’s digit, which we obtained from 576. 

Step 4: So the cube root of number 17576 will be 26. 

26^3 = 17576.

Mixed bag problems: 

Example 1: Solve the cube root of 46656 by the method of estimation.

Solution: We have to find the cube root of 46656

Step 1: We will separate the number into pair of three numbers from backward

Here, 46 and 656 are a set of two pairs. 

Step 2: Let us take the number 656 first, 

Unit digit of the number 656 is 6. 

You have to refer to the above table and check what’s in the unit place, which ends with the number 6. From the table, we understand that the cube of the number 6 always ends with the number 6 at the unit’s place. We will fix 6 as our last digit. Remember this! We will use it later.

Step 3: Now, it is time to take the remaining numbers i.e. 46 

From the table, we notice that the number 46 falls between 3^3= 27 and 4^3= 64. Now, select the smallest cube which is 27. See 27 is the cube root of which number. It is 3. Thus, 3 is the other needed number, which will go in ten’s place.  

Step 4: So the cube root of a number 46656 is 36. 

Example 2: Can you find the cube root of 1061208  by the method of estimation.

 Solution: Here, the given number is 1061208 - a 7-digit number.

Step 1: We will separate the number into pair of three numbers from backward

Here, 208 and 1061 are a set of two pairs. 

Step 2: Let us take the number last three-digit, that is,  208.

Unit digit of the number 208 is 8. 

You have to refer to the above table and check what’s in the unit place, which ends with the number 8. From the table, we understand that the cube of the number 2 always ends with the number 8 at the unit’s place. We will fix 2 as our last digit. Remember this! We will use it later.

Step 3: Now let us take 1061 

1061 falls between 10^3= 1000  and 11^3= 1331.

From the table, we notice that the number 1061 falls between 10^3= 1000 and 11^3= 1331. Now, select the smallest cube which is 1000. See 1000  is the cube root of which number. It is 10. Thus, 10 is the other needed number.  

Since 1061 falls between the cube of 10 and 11, we will take the smaller number as the cube of 10. 10^3=1000.

So, the number is 10 here.

Step 4: So the cube root of 1061208 is 102.